Some thick brane solutions in $f(R)$-gravity

Abstract

The thick brane model is considered in $f(R)\sim R^n$ gravity. It is shown that regular asymptotically anti-de Sitter solutions exist in some range of values of the parameter $n$. A peculiar feature of this model is the existence of a fixed point in the phase plane where all solutions start, and the brane can be placed at this point. The presence of the fixed point allows to avoid fine tuning of the model parameters to obtain thick brane solutions.